1. Field of the Invention
The present invention relates to a mobile communication system, and more particularly to an apparatus and a method for selecting and transmitting a transmission eigenvector in a closed loop multi input multi output (MIMO) mobile communication system.
2. Description of the Related Art
Generally, in a 4G (4th Generation) communication system, which is the next generation communication system, research is ongoing to provide users with services having various quality of service (‘QoS’) and supporting a transmission speed of about 100 Mbps. Currently, the 3G (3rd Generation) communication system supports a transmission speed of about 384 kbps in an outdoor channel environment having a relatively unfavorable channel environment, and supports a maximum transmission speed of 2 Mbps in an indoor channel environment having a relatively favorable channel environment.
A wireless local area network (LAN) system and a wireless metropolitan area network (MAN) system generally support transmission speeds of 20 to 50 Mbps. Further, the 4G communication system has been developed to ensure mobile station mobility and QoS in the wireless LAN system and the wireless MAN system supporting relatively high transmission speeds. Accordingly, research is ongoing to develop a new communication system capable of supporting a high speed service to be provided by the 4G communication system.
To provide the high speed service (i.e., wireless multimedia service), a broadband spectrum is used. Inter-symbol interference may occur due to a multi-path propagation. The inter-symbol interference may deteriorate the entire transmission efficiency of a system. To compensate for the inter-symbol interference due to the multi-path propagation as described above, an orthogonal frequency division multiplexing (OFDM) scheme has been proposed. In the OFDM scheme, an entire frequency band is divided into a plurality of subcarriers and the subcarriers are transmitted. When the OFDM scheme is used, one symbol duration may increase. Accordingly, the inter-symbol interference can be minimized.
Further, the OFDM scheme is a scheme for transmitting data using multiple carriers and is a special type of a Multiple Carrier Modulation (MCM) scheme in which a serial symbol sequence is converted into parallel symbol sequences and the parallel symbol sequences are modulated with a plurality of mutually orthogonal subcarriers before being transmitted.
In relation to the OFDM scheme, in 1971, Weinstein, et al. proposed that the OFDM modulation/demodulation can be efficiently performed using Discrete Fourier Transform (DFT), which was a driving force behind the development of the OFDM scheme. Also, the introduction of a guard interval and a cyclic prefix as the guard interval further mitigates the adverse effects of the multipath propagation and the delay spread on systems. Although hardware complexity was an obstacle to the widespread implementation of the OFDM scheme, recent advances in digital signal processing technology including fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) have enabled the OFDM scheme to be implementation in a less complex manner.
The OFDM scheme, similar to an existing Frequency Division Multiplexing (FDM) scheme, boasts of an optimum transmission efficiency in a high-speed data transmission because the OFDM transmits data on subcarriers, while maintaining orthogonality among them. The optimum transmission efficiency is further attributed to good frequency use efficiency and robustness against multipath fading in the OFDM scheme. More specifically, overlapping frequency spectrums lead to efficient frequency use and robustness against frequency selective fading and multipath fading. The OFDM scheme reduces effects of ISI through the use of guard intervals and enables the design of a simple equalizer hardware structure. Furthermore, because the OFDM scheme is robust against impulse noise, it is increasingly popular in communication systems.
A Multiple Access scheme based on the OFDM scheme is an orthogonal frequency division multiple access (OFDMA) scheme. In the OFDMA scheme, some of the subcarriers are reconstructed into a subcarrier set and the subcarrier set is assigned to a specific mobile subscriber station (MSS). In the OFDMA scheme, it is possible to perform a dynamic resource allocation capable of dynamically allocating a subcarrier set assigned to a specific mobile subscriber station according to fading of a wireless transmission path.
Further, for high speed data transmission, methods using a multiple antenna in both a transmitter and a receiver have been developed. Starting from a space time coding (STC) method proposed by Tarokh in 1997, a Bell Lab Layered Space Time (BLAST) method devised by Bell Laboratories has been proposed. In particular, since the BLAST method has a transmission rate linearly increased in proportion to the number of transmission/reception antennas, it has been applied to a system targeting high speed data transmission.
Existing BLAST algorithms have been used in an open loop method. In such a case, since the aforementioned dynamic resource allocation is impossible, a closed loop method has been recently devised. Among the BLAST algorithms, a representative algorithm is the algorithm for a singular value decomposition multi input multi output (SVD-MIMO) system, in which a matrix-type channel is converted into channels corresponding to the number of virtual transmission/reception antennas by using an SVD technology used in a linear algebra.
The SVD technology will be briefly described to aid in the understanding of the SVD-MIMO system.
Before a description on the SVD technology is given, an eigenvalue decomposition (EVD) will be described. When the product of a m×m square matrix A by a predetermined vector χ having a size of m×1 is equal to the product λχ of a complex number λ by the vector χ, Equation 1 may be obtained.A χ=λχ  (1)
In Equation 1, the λ denotes an eigenvalue of matrix A and the χ denotes an eigenvector. In order to obtain the vector λ, the λ satisfying Equation 2 is determined.det(A−λI)=0   (2)
In Equation 2, the det denotes a determinant of a matrix. The vector χ satisfying Equation 1 is determined from the λ obtained from Equation 2. For instance, Equation 3 is used to calculate eigenvalues and eigenvectors for a matrix
                                                        A              =                            ⁢                                                                    [                                                                                            4                                                                                                      -                            5                                                                                                                                                2                                                                                                      -                            3                                                                                                                ]                                    ·                  det                                ⁢                                                                  ⁢                                  (                                      A                    -                    λI                                    )                                                                                                        =                            ⁢                              det                ⁡                                  [                                                                                                              4                          -                          λ                                                                                                                      -                          5                                                                                                                                    2                                                                                                                          -                            3                                                    -                          λ                                                                                                      ]                                                                                                                        =                                ⁢                                                                            λ                      2                                        -                    λ                    -                    2                                    =                  0                                            ;                                                                                                            λ                  1                                =                                ⁢                                  -                  1                                            ,                                                λ                  2                                =                2                                                                        (        3        )            
In Equation 3, the eigenvectors for the λ1=−1 and the λ2=2 can be calculated by Equations 4 and 5.
                                                        (                              A                -                                  λ                  ⁢                                                                          ⁢                  I                                            )                        ⁢            x                    =                                                    [                                                                            5                                                                                      -                        5                                                                                                                        2                                                                                      -                        2                                                                                            ]                            ⁡                              [                                                                            y                                                                                                  z                                                                      ]                                      =                          [                                                                    0                                                                                        0                                                              ]                                      ;                              x            1                    =                      [                                                            1                                                                              1                                                      ]                                              (        4        )                                                                    (                              A                -                                  λ                  ⁢                                                                          ⁢                  I                                            )                        ⁢            x                    =                                                    [                                                                            2                                                                                      -                        5                                                                                                                        2                                                                                      -                        5                                                                                            ]                            ⁡                              [                                                                            y                                                                                                  z                                                                      ]                                      =                          [                                                                    0                                                                                        0                                                              ]                                      ;                              x            2                    =                      [                                                            5                                                                              2                                                      ]                                              (        5        )            
A method for calculating the eigenvectors as described above may be summarized according to the following steps:                step 1) calculate the determinant of the (A−λI);        step 2) calculate a root of step 1) and calculate eigenvalues; and        step 3) calculate eigenvectors satisfying the Aχ=λχ for the eigenvalues calculated in step 2).        
When the calculated eigenvectors are linearly independent from each other, the matrix A may be reconstructed by means of the calculated eigenvalues and eigenvectors. A matrix D may be defined by Equation 6, in which the eigenvalues are employed as diagonal elements, and the remaining elements, except for the diagonal elements, are 0.
                    D        =                  [                                                                      λ                  1                                                            0                                            ⋯                                            0                                                                    0                                                              λ                  2                                                            ⋯                                            0                                                                    ⋮                                            ⋮                                            ⋯                                            ⋮                                                                    0                                            0                                            ⋯                                                              λ                  m                                                              ]                                    (        6        )            
Further, a matrix S arranging the aforementioned eigenvectors in a column may be defined by Equation 7.S=[x1 x2 . . . xm]  (7)
When matrix A is defined on the basis of matrix D defined by Equation 6, and matrix S defined by Equation 7, matrix A may be expressed by Equation 8.A=SΛS−1   (8)
When the aforementioned example is applied to Equation 8, the
  A  =    ⁢      [                            4                                      -            5                                                2                                      -            3                                ]  may be expressed by Equation 9.
                    A        =                ⁢                              [                                                            4                                                                      -                    5                                                                                                2                                                                      -                    3                                                                        ]                    =                    ⁢                                                                      [                                                                                    1                                                                    5                                                                                                            1                                                                    2                                                                              ]                                ⁢                                   [                                                                                                    -                        1                                                                                    0                                                                                                                                                                                                    ⁢                        0                                                                                    2                                                                      ]                            ⁢                               [                                                                    1                                                        5                                                                                        1                                                        2                                                              ]                                      -              1                                                          (        9        )            
Hereinafter, the SVD will be described based on the aforementioned EVD.
First, the EVD can be obtained only for a square matrix. Accordingly, a method similar to the EVD may be used for a m×n matrix which is not a square matrix. That is, when a matrix B, which is not a square matrix, is defined, matrix B may be factorized as expressed by Equation 10.B=UDVH   (10)
In Equation 10, the U is the aforementioned m×m unitary matrix and the eigenvectors of a BBH constitute the columns of the U. The eigenvectors of a BHB constitute the columns of the V which is a n×n matrix. Further, singular values (diagonal elements of the matrix D) are square roots of the values (except for 0) among the eigenvalues of the BBH or the BHB.
The aforementioned SVD can be applied to the MIMO system by the following method.
When it is assumed that the number of transmission antennas is NT and the number of reception antennas is NR in the MIMO system, a channel H carrying data transmitted from a transmitter until the data are received in a receiver may become a random matrix of NR×NT. In such a case, when the channel matrix H is separated through the SVD scheme, the matrix H may be expressed by Equation 11.H=UDVH   (11)
In Equation 11, the U is a NR×NR unitary matrix and the eigenvectors of a HHH constitute the columns of the U. The U will be referred to as a reception eigenvector matrix. Further, the eigenvectors of a HHH constitute the columns of the V which is a NT×NT matrix and the V will be referred to as a transmission eigenvector matrix. Further, the singular values (diagonal elements of the matrix D) are the square roots of the values (except for 0) among the eigenvalues of the HHH or the HHH. The D will be referred to as a singular value matrix. Further, the operator H used as a superscript denotes a complex conjugate transpose operation (Hermitian).
A communication system using a multiple antenna may be generally expressed by Equation 12.Y=HX+N   (12)
In Equation 12, the Y denotes a reception symbol matrix of a NR×1 and the X denotes a transmission symbol matrix of a NT×1. Further, the H denotes a channel matrix of a NR×NT and the N denotes an additive white Gaussian noise (AWGN) matrix of the NR×1. The symbol matrix X to be transmitted is transmitted through the channel of the matrix H. The symbol matrix X is transmitted to a receiver, and includes the matrix N which is noise component.
The SVD-MIMO system will be described by use of the aforementioned SVD scheme.
When a transmitter uses a pre-filter such as a matrix V, the transmission symbol matrix X may be expressed by Equation 13.X′=V·X   (13)
Further, when a receiver uses a post-filter such as a matrix UH, the reception symbol matrix Y may be expressed by Equation 14.Y′=UH·Y   (14)
Accordingly, the SVD-MIMO system in which the transmitter uses the matrix V as a pre-filter and the receiver uses the matrix UH as a post-filter may be expressed by Equation 15.
                                                                        Y                ′                            =                            ⁢                                                                    U                    H                                    ·                  Y                                =                                                                            U                      H                                        ⁢                    HVX                                    +                                                            U                      H                                        ⁢                    N                                                                                                                          =                            ⁢                                                                    U                    H                                    ⁢                                      UDV                    H                                    ⁢                  VX                                +                                                      U                    H                                    ⁢                  N                                                                                                        =                            ⁢                              DX                +                                                      U                    H                                    ⁢                  N                                                                                        (        15        )            
When Equation 15 is decomposed according to each element of each matrix, Equation 15 may be expressed as Equation 16. For convenience of description, it is assumed that NT≦NR.
                              Y          ′                =                              [                                                                                y                    1                    ′                                                                                                                    y                    2                    ′                                                                                                ⋮                                                                                                  y                                          N                      R                                        ′                                                                        ]                    =                                                    [                                                                                                    λ                        1                                                                                    0                                                              ⋯                                                              0                                                                                                  0                                                                                      λ                        2                                                                                    ⋯                                                              0                                                                                                  ⋮                                                              ⋮                                                              ⋯                                                              ⋮                                                                                                  0                                                              0                                                              ⋯                                                                                      λ                                                  N                          T                                                                                                                    ]                            ⁡                              [                                                                                                    x                        1                                                                                                                                                x                        2                                                                                                                        ⋮                                                                                                                          x                                                  N                          T                                                                                                                    ]                                      +                          [                                                                                          n                      1                      ′                                                                                                                                  n                      2                      ′                                                                                                            ⋮                                                                                                              n                                              N                        R                                            ′                                                                                  ]                                                          (        16        )            
As expressed by Equation 16, in the SVD-MIMO, a system transmitting data from a plurality of transmission antennas to a plurality of reception antennas may be regarded as a multiple single input single output (SISO) system. That is, the channel matrix H may be simplified as a channel D including diagonal elements, which are eigenvalues having a less smaller than or equal to min (NT, NR), by the processing of a matrix V in the transmitter and the processing of a matrix UH in the receiver. As described above, in a state in which the channel H is rearranged by use of the SVD scheme, the transmitter uses a preprocessor and the receiver uses a post-processor, if the transmitter only determines the eigenvector V value, an MIMO channel can be simplified into a plurality of SISO channels for easy analysis. Further, as described above, the SVD-MIMO system changes into plural SISO systems employing the λi as channel values. The transmitter can perform an optimal dynamic allocation on the basis of the predetermined V and λi. In such a case, the receiver must transmit to the transmitter information related to the V and information related to the λi.
An OFDM system employing the aforementioned SVD scheme will be described with reference to FIG. 1.
FIG. 1 is a block diagram of an MIMO system employing an SVD-MIMO scheme according to the prior art.
FIG. 1 shows an example in which the SVD-MIMO scheme is applied to the OFDM system. It is noted that the SVD-MIMO scheme can also be applied to other communication systems, which employ a code division multiple access (CDMA), a time division multiple access (TDMA) or a frequency division multiple access (FDMA), etc., in addition to the OFDM system employing the MIMO.
Data to be transmitted by a transmitter are encoded by a predetermined channel encoder, etc., before being transmitted. For convenience of description, a process after the encoding will be described with reference to FIG. 1.
Referring to FIG. 1, when the encoded data is parallel-converted by a serial-to-parallel (S/P) converter 101, the channel matrix H as described above is multiplied by the matrix V of Equation 1, for which the SVD has been performed, in a preprocessing operator 103. Each calculation result obtained through the multiplication with the matrix V is subjected to an inverse fast Fourier transform (IFFT) through a plurality of IFFT units 105a to 105n mapped to a plurality of transmission antennas, and is then transmitted to a receiver through a plurality of parallel-to-serial converters 107a to 107n and a plurality of transmission antennas 109a to 109n. 
The signals transmitted through the plurality (e.g., NT) of transmission antennas 109a to 109n in a transmitter can be received through a plurality (e.g., NR) of reception antennas 111a to 111n in the receiver. That is, the signals transmitted from the first transmission antenna 109a can be received at each of the NR reception antennas. Herein, the signals received in each reception antenna are received through different channels. Similarly, the signals transmitted from the second transmission antenna or the NT transmission antenna can be received through the NR reception antennas. Accordingly, the transmission channel H may be expressed by Equation 17 according to the channels between the transmission antennas and the reception antennas.
                    H        =                  [                                                                      H                  11                                                                              H                  12                                                            ⋯                                                              H                                      1                    ⁢                    N                                                                                                                        H                  21                                                                              H                  22                                                            ⋯                                                              H                                      2                    ⁢                    N                                                                                                      ⋯                                                                                                                                                                                                                                                                                                                                H                  M1                                                                              H                  M2                                                            ⋯                                                              H                  MN                                                              ]                                    (        17        )            
The signals transmitted through the transmission channel H are received through each of the NR reception antennas. The signals received through each of the reception antennas are parallel-converted through serial-to-parallel converters 113a to 113m and are then subjected to an FFT through FFT units 115a to 115m. Then, the received signals for which the FFT has been performed are multiplied by a matrix UH by the aforementioned SVD scheme in a post-processing operator 117 and are then serial-converted by a parallel-to-serial (P/S) converter 119.
Meanwhile, the receiver of the SVD-MIMO system estimates channel values transmitted from the multiple transmission antenna to the multiple reception antenna, obtains the matrices V, D and U of the matrix H by use of the SVD scheme, and feedbacks the obtained information to the transmitter. When the matrices V and D are transmitted from the receiver to the transmitter, the transmitter can use an optimal resource allocation algorithm according to the channel conditions on the basis of the λi which is the diagonal elements of the matrix D and is the singular value of the channel H.
However, in such a case, since the receiver must feedback both the matrices V and D to the transmitter, a large quantity of feedback information is required. Further, the SVD system may transmit data through a channel having a small value among eigenvalues which are elements of the matrix D. In such a case, the error probability increases, thereby rapidly deteriorating the transmission efficiency of data. Accordingly, it is necessary to provide a method capable of more efficiently performing data transmission in the SVD-MIMO system.